Adding Matter to Poincaré Invariant Branes

A solution to the cosmological constant problem has been proposed in which our universe is a 3-brane in a 5-dimensional spacetime. With a bulk scalar, the field equations admit a Poincare invariant brane solution regardless of the value of the cosmological constant (tension) on the brane. However, the solution does not include matter in the brane. We show that adding matter as a perturbation leads to static cosmology. Furthermore, we find new exact static solutions with matter density and pressure in the brane. Small perturbations about these solutions are time dependent, but inconsistent with observational cosmology. As a byproduct we find a class of new matterless static solutions and a non-static solution which, curiously, requires the string value for the dilaton coupling